Computers & Mathematics with Applications ( IF 2.9 ) Pub Date : 2020-06-01 , DOI: 10.1016/j.camwa.2020.05.019 Yang Cao , Zhen-Quan Shi , Quan Shi
By introducing a regularization matrix and an additional iteration parameter, a new class of regularized deteriorated positive-definite and skew-Hermitian splitting (RDPSS) preconditioners are proposed for generalized saddle point linear systems. Compared with the well-known Hermitian and skew-Hermitian splitting (HSS) preconditioner and the regularized HSS preconditioner (Bai, 2019) studied recently, the new RDPSS preconditioners have much better computing efficiency especially when the (1,1) block matrix is non-Hermitian. It is proved that the corresponding RDPSS stationary iteration method is unconditionally convergent. In addition, clustering property of the eigenvalues of the RDPSS preconditioned matrix is studied in detail. Two numerical experiments arising from the meshfree discretization of a static piezoelectric equation and the finite element discretization of the Navier–Stokes equation show the effectiveness of the new proposed preconditioners.
中文翻译:
广义鞍点线性系统的正则化DPSS预处理器
通过引入一个正则化矩阵和一个附加的迭代参数,针对广义鞍点线性系统,提出了一类新的正则化恶化正定和偏Hermitian分裂(RDPSS)预处理器。与最近研究的著名的Hermitian和Skew-Hermitian分裂(HSS)预处理器和正则化HSS预处理器(Bai,2019)相比,新的RDPSS预处理器具有更好的计算效率,尤其是在(1,1)块矩阵不为-埃尔米蒂安。证明了相应的RDPSS平稳迭代方法是无条件收敛的。此外,还详细研究了RDPSS预处理矩阵特征值的聚类性质。